show · nf.ideal_class_group all knowls · up · search:

The ideal class group of a number field $K$ with ring of integers $O_K$ is the group of equivalence classes of ideals, given by the quotient of the multiplicative group of all fractional ideals of $O_K$ by the subgroup of principal fractional ideals.

Since $K$ is a number field, the ideal class group of $K$ is a finite abelian group, and so has the structure of a product of cyclic groups encoded by a finite list $[a_1,\dots,a_n]$, where the $a_i$ are positive integers with $a_{i+1}\mid a_i$ for $1\le i<n$.

Knowl status:
  • Review status: reviewed
  • Last edited by Holly Swisher on 2019-04-26 14:26:25
Referred to by:
History: (expand/hide all) Differences (show/hide)